Exergy and Irreversible Entropy Production Thermodynamic Concepts for Control Design: Nonlinear Systems

This paper develops a novel control system design methodology that uniquely combines: concepts from thermodynamic exergy and entropy; Hamiltonian systems; Lyapunov´s direct method and Lyapunov optimal analysis; electric AC power concepts; and power flow analysis. Relationships are derived between exergy/entropy and Lyapunov optimal functions for Hamiltonian systems. The methodology is demonstrated with two fundamental numerical simulation examples: 1) a Duffing oscillator/Coulomb friction nonlinear model that employs PID regulator control and 2) a van der Pol nonlinear oscillator system. The control system performances and/or appropriately identified terms are partitioned and evaluated based on exergy generation and exergy dissipation terms. This novel nonlinear control methodology results in both necessary and sufficient conditions for stability of nonlinear systems